I actually believe that the Illusive Man's road to indoctrination began when his eyes did become that way, which was in the graphic novel in his past during the first contact war. Or just after, I forget. Still though, he and Saren were effected by a mysterious device that ma have been an old reaper artifact. May have just made him more susceptible too.

As far as we know of Indoctrination, one gets affected if you stay too long in close proximity, or if you get in direct contact with Reaper Technology.

In case of TIM, he was indoctrinated shortly after Shanxi around 2157 during the events of the grafic novel ME: EVOLUTION. It functions as a backstory for him and we get to know his real name.

Anyway he got in direct contact with a very aggressive Reaper Tech and as a result he got is eyes transformed by Reaper Nanobots.

Indoctrination is sublte... the longer it takes, the deeper it gets and the longer the victim thinks he is still in charge of himself.

As for TIM, the Indoctrination first manifested as his ultima credo.... advance humanity at any cost to fight the reapers... though we know that this advancement is part of the Reaper Invasion, as referring o Javik and die VI Vendetta, there where Reaper Controlling focus but indoctrinated splinter groups within the Prothean Society aswell, just like Cerberus was for us.

TL:DR

He was indoctrinated around 2157 on Palaven while touching a Reaper Artifact.

Obviously I have some interesting things to read. That settled. After Peaceable Kingdoms I start ME book marathon no matter what.

Edited my initial reply and removed obviously wrong part. In my defence I was more thinking about =Transformation= from last ME3 scene, that TIM-reaper hybrid, not indoctrination per se. Sorry for that.